The present invention relates to data processing, more particularly to data reduction in correspondence with parametric relationships.
In the past, efforts to fit both linear and nonlinear parametric relationships to experimental data have relied heavily upon transformations and approximations that stem directly from or can be derived as traditional forms of least-squares regression analysis. The basic concepts typical of the procedure were first formally enunciated in 1805 in a paper by A. M. Legendre who utilized the associated techniques in a study of certain astronomical observations. Similar techniques were independently developed and considered as early as 1795 by C. F. Gauss. Both bivariate and multivariate forms of the traditional least-squares regression analysis are valid for linear data reduction applications when errors are limited to nonskewed variations in a single variable parameter.
The present invention provides conformal analysis as an optional replacement for traditional regression analysis. It also provides explicit form for composite coordinate normalizing coefficients which are included as weight factors, which are composed of coordinate normalizing proportions, unique to each datum and corresponding rectified form, which make it possible to expand bivariate and multivariate, regression analysis and conformal analysis to provide improved forms of linear and nonlinear multidimensional data processing. The present invention represents major breakthroughs in multivariate statistical analysis and automatic data processing. Alternate reduction procedures are disclosed and employed to account for nonuniform error distributions, variations in precision uncertainties, and errors in more than a single variable parameter. Automated or semi-automated processes providing the expanded analysis capabilities are referred to by the inventor as discriminate reduction data processing. Adaptation is considered for use of discriminate reduction data processing to provide velocity dependent representations of non-stationary multiple frequency band hydroacoustic sound pressure data.